If you need to do this conversion in PHP, as part of whatever import process, then you can just convert the comma-separated values into an array with explode(), and then use update_post_meta(), which will automatically serialise the value for you:
$value="Morning,Daytime";
$array = explode( ',', $value );
update_post_meta( $post_id, 'hours_of_operation', $array );
Use trim() if your comma separated values include, or could include, spaces:
$value="Morning, Daytime";
$array = explode( ',', $value );
$array = array_map( 'trim', $array );
update_post_meta( $post_id, 'hours_of_operation', $array );
If, for whatever reason, you need to serialise the value yuorself in PHP, you can use serialize() to convert the array to a serialised string.
$value="Morning,Daytime";
$array = explode( ',', $value );
$serialized = serialize( $array );